The 25-year-old Canadian star will join returning actors Vin Diesel and Karl Urban on the project, which is rumoured to bear the subtitle Dead Man Stalking, reports Variety.
Jordi Molla previously signed up to portray the movie's villain Santana, while Battlestar Galactica's Katee Sackhoff will play Nordic mercenary Dahl.
Funk's role in the third Riddick film is yet to be announced. He is best known for playing Conrad Birdie in the Broadway musical Bye Bye Birdie, and has appeared in numerous television and film projects of late.
Chronicles of Riddick's second sequel resumed production in December last year after budget issues stopped it in its tracks. Diesel previously revealed that it will be R-rated.
The film is expected to be released in 2013.
Watch a trailer for The Chronicles of Riddick below: